Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ?

**kkm** · June 19th 2012, 05:28 AM

Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ? What kind of factorization is used here?

**Prove It** · June 19th 2012, 05:36 AM

It looks like a factorisation by grouping...

$\displaystyle \begin{align*} 2x^2 - xy - 3y^2 &= 2x^2 - 3xy + 2xy - 3y^2 \\ &= x(2x - 3y) + y(2x - 3y) \\ &= (2x - 3y)(x + y) \end{align*}$

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Why is 2x^2-xy-3y^2 = (2x - 3y)(x + y) ?

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